Multiple choice

Sum of the angles made by a chord at the Centre and on the major arc of a circle is 180 degree. What will be the angle made at the Centre of the circle?

  1. 60 degree

  2. 90 degree

  3. 75 degree

  4. 120 degree

Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Let the angle at the centre be C and at the major arc be M. Given: C + M = 180°. For any chord, the angle at the centre is twice the angle at the circumference on the same side: C = 2M. Substituting: 2M + M = 180°, so 3M = 180°, M = 60°. Therefore, C = 180° - 60° = 120°. The angle at the centre is 120°.